YES(?,O(n^1))

Problem:
 d(x) -> e(u(x))
 d(u(x)) -> c(x)
 c(u(x)) -> b(x)
 v(e(x)) -> x
 b(u(x)) -> a(e(x))

Proof:
 Complexity Transformation Processor:
  strict:
   d(x) -> e(u(x))
   d(u(x)) -> c(x)
   c(u(x)) -> b(x)
   v(e(x)) -> x
   b(u(x)) -> a(e(x))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [a](x0) = x0,
     
     [v](x0) = x0,
     
     [b](x0) = x0 + 1,
     
     [c](x0) = x0,
     
     [e](x0) = x0,
     
     [u](x0) = x0,
     
     [d](x0) = x0
    orientation:
     d(x) = x >= x = e(u(x))
     
     d(u(x)) = x >= x = c(x)
     
     c(u(x)) = x >= x + 1 = b(x)
     
     v(e(x)) = x >= x = x
     
     b(u(x)) = x + 1 >= x = a(e(x))
    problem:
     strict:
      d(x) -> e(u(x))
      d(u(x)) -> c(x)
      c(u(x)) -> b(x)
      v(e(x)) -> x
     weak:
      b(u(x)) -> a(e(x))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [a](x0) = x0,
       
       [v](x0) = x0,
       
       [b](x0) = x0 + 1,
       
       [c](x0) = x0,
       
       [e](x0) = x0 + 1,
       
       [u](x0) = x0,
       
       [d](x0) = x0
      orientation:
       d(x) = x >= x + 1 = e(u(x))
       
       d(u(x)) = x >= x = c(x)
       
       c(u(x)) = x >= x + 1 = b(x)
       
       v(e(x)) = x + 1 >= x = x
       
       b(u(x)) = x + 1 >= x + 1 = a(e(x))
      problem:
       strict:
        d(x) -> e(u(x))
        d(u(x)) -> c(x)
        c(u(x)) -> b(x)
       weak:
        v(e(x)) -> x
        b(u(x)) -> a(e(x))
      Matrix Interpretation Processor:
       dimension: 1
       max_matrix:
        1
        interpretation:
         [a](x0) = x0 + 1,
         
         [v](x0) = x0,
         
         [b](x0) = x0,
         
         [c](x0) = x0 + 1,
         
         [e](x0) = x0,
         
         [u](x0) = x0 + 1,
         
         [d](x0) = x0 + 1
        orientation:
         d(x) = x + 1 >= x + 1 = e(u(x))
         
         d(u(x)) = x + 2 >= x + 1 = c(x)
         
         c(u(x)) = x + 2 >= x = b(x)
         
         v(e(x)) = x >= x = x
         
         b(u(x)) = x + 1 >= x + 1 = a(e(x))
        problem:
         strict:
          d(x) -> e(u(x))
         weak:
          d(u(x)) -> c(x)
          c(u(x)) -> b(x)
          v(e(x)) -> x
          b(u(x)) -> a(e(x))
        Matrix Interpretation Processor:
         dimension: 1
         max_matrix:
          1
          interpretation:
           [a](x0) = x0,
           
           [v](x0) = x0,
           
           [b](x0) = x0,
           
           [c](x0) = x0 + 1,
           
           [e](x0) = x0,
           
           [u](x0) = x0,
           
           [d](x0) = x0 + 1
          orientation:
           d(x) = x + 1 >= x = e(u(x))
           
           d(u(x)) = x + 1 >= x + 1 = c(x)
           
           c(u(x)) = x + 1 >= x = b(x)
           
           v(e(x)) = x >= x = x
           
           b(u(x)) = x >= x = a(e(x))
          problem:
           strict:
            
           weak:
            d(x) -> e(u(x))
            d(u(x)) -> c(x)
            c(u(x)) -> b(x)
            v(e(x)) -> x
            b(u(x)) -> a(e(x))
          Qed